Good description, but I would say even the parallel and seemingly rational analysis can be very one sided. I noticed on myself that in similar situations my "rational" analysis swings in the same direction as my mood. And if it doesn't, I sometimes do not believe, or more precisely, do not feel it. So it doesn't really help quite a lot. This doesn't make it useless, just a side note to not be to harsh on yourself if it doesn't work.

Another thing which also helps me in such situations, is to remember these are just feelings. Sometimes you just feel worthless or dumb, but this are just your feelings, not you. And just because you feel this way, it doesn't need to be true. Acknowledge the feeling, but try to still notice it is just a feeling.